Ok first of you are going to think: "Oh look a lane Amumu OMG man go jungle you noob".
But a lane amumu isnt that bad, there are a lot of champions in the game that can own with him in a lane, so lets start.

Pros:
Has good CC.
Great in team fights.
A tank that deals damage.
Easy to farm, good AoE.
Cons:
Blue dependent.
Really weak early.
Doesn't really have that sustain until mid/late game.
Allies dependent.

Ok for runes i take 12(marks+quintesences) magic penetration runes,(glyph) 9 cd reduction runes,9(seal) Ability power runes.
I take magic penetration over armor because you have insane dps early game with all your skills, cd reduction runes because amumu with a high cd ultimate isn't a good amumu, and ability power runes for more damage output. Just remember with this build your not just a tank but a dps also.

i take 9 0 21 masteries because amumu needs low cooldowns, mana, mana regen.
I used to go with 0 21 9 sets but this is less efficient. It's really up to the player. If you need survivability take the 0 21 9.

For items i start of with hp regeneration and a heal.
Later on i don't go to base without at least 1.4k gold because its just enough for your boots of swiftness and Philosofer's stone. Later on i buy sunfire cape as soon as posible because it stacks really good with your other aoe abilities and gives good armor and hp.
Once you have sunfire cape farming will be a snap and you will easily get Shurelya's Reviere, Aegis of the legion, Frozen hearth and Rilays scepter.
Rilays scepter is a great item for amumu because all your abilites slow the target(s). if your having trouble wit ap carries get force of nature and sell aegis.

Now i know that its stupid not to level E, because it will make you more tanky and stuff, but time after time i found W to be much more usefull because it can't be silenced if it was active, u will cry even thou you are stunned, it has a low mana cost, and is better if your fighting either tanks or mages that dont atack you very often. Only if your up against 2 meeele atack damage dpss should you level E.

Farming is a snap with amumu because all your abilities are AOE eccept for Q, and your E gets reduced every time you are hit by 0.5 sec. And offcourse lets not forget the importance of the blue buff for amumu. It gives me great mana regeneration and low cd all the stuff amumu needs.

Amumu is relatively a solid jungler however i don't like recommend it for one reason: He is blue dependent as i said so in the cons above. Thing is he is not like the other junglers like warvick,tryndamere,... If you are killed while attempting to kill the blue buff or the enemy team just steals it, it will be agonising for you to recover from that. But if you manage to pull it of, you will be all right since you have good AoE skills and your E reduces damage taken from creeps.

I take ghost for nearly every champion because it's the most useful spell of all(chasing running away) and ignite for a finishing skill. Since you are a lane amumu and you don't take smite this is the best summoner spell for you. A summoner spell to consider is Exhaust because it's great in a team fight for disabling any carry. It's really up to you. Or if your not fond of ghost just go with flash -.- ;

[*] Amumu should always enter a team battle first and use his ultimate to get the most amount of enemy heroes in it. Remember don't use your ulti unless all your allies are near you when you use it and dont use it for less than 2-3 targets unless you are trying to save someone.
Always remember before using your ultimate to at least attacks 1 enemy hero because of your passive. And now some heroes that go with amumu:

Morgana the apsolute monster with amumu in a lane. If your teammate is a good morgana it's a deadly combo.
Sion AP or AD he is a grat choice in a lane because you have 2 stuns, both of you are tanky and great dpss.
Jax, Master yi and Nunu also great champions in a lane with you because of their damage output .

Ok so your in ranked and your an amumu. your job is to initate first and disable the ad/ap carry and Ulti as many oppoents as you can. To do so you need to stay with your team and work your way through the fights. It's not that difficult once you get the hang of it just keep in mind that your as good as your allies are.

The unique thing about this guide is that you don't see many amumu's going solo top or bot with a support. But trust me this build works and i would have shown you the proof unfortunatly i haven't screen-shoted any of my amumu games so sorry about that. Your just going to have to trust me on this.

That's it rally hope it helps and sorry for not having any pictures i didn't know how to do it considering it was my first guide.